In this implementation of pix2pix, why are the weights for the discriminator and generator losses set to 1 and 100 respectively?
After further research, I have found the answer. nbro was of course right, the weighting is not implementation dependant, it was already introduced in the paper (arXiv). However, there is minimal information about that, only it is mentioned within the optimization function:
$\arg \min_G \max_D \mathcal{L}_{cGAN}(G,D) + \lambda \mathcal{L}_{L1}(G)$
In fact, the parameter lambda stands for weight of $L_1$ loss. There should be a second parameter $\epsilon$ for $\mathcal{L}_{cGAN}(G,D)$ because in real implementation you can actually change that as well. In theory, however, only modulation of $L_1$ loss is needed. The paper does not state why the $\lambda$ parameter is needed, only mentions that setting it to 0 will lead to pure cGAN implementation. David Brownlee in his blog states:

The adversarial loss influences whether the generator model can output
images that are plausible in the target domain, whereas the L1 loss
regularizes the generator model to output images that are a plausible
translation of the source image. As such, the combination of the L1
loss to the adversarial loss is controlled by a new hyperparameter
lambda, which is set to 10, e.g. giving 10 times the importance of the
L1 loss than the adversarial loss to the generator during training.

The loss weights thus are hyperparameters that tell the network how much plausible translation of the source image do we need.